Abstract
We show that if $\mathbf{X} = (X_1,\ldots,X_d)$ is a vector in $\mathbb{R}^d$ and all linear combinations $\sum^d_{i=1}C_iX_i$ are 1-stable random variables, then $\mathbf{X}$ is itself 1-stable. More generally, a probability measure $\mu$ on a vector space whose univariate marginals are 1-stable is itself 1-stable. This settles an outstanding problem of Dudley and Kanter.
Citation
Gennady Samorodnitsky. Murad S. Taqqu. "Probability Laws with 1-Stable Marginals are 1-Stable." Ann. Probab. 19 (4) 1777 - 1780, October, 1991. https://doi.org/10.1214/aop/1176990235
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